



01595nas a2200145   4500008004100000245005500041210005500096260001300151520116600164100002301330700002001353700002201373700001701395856003701412       2024                        eng d00aTopology and entanglement of molecular phase space0 aTopology and entanglement of molecular phase space  c3/7/20243 a<p>We formulate a quantum phase space for molecular rotational and nuclear-spin states. Taking in molecular geometry and nuclear-spin data, our framework yields admissible position and momentum states, inter-convertible via a generalized Fourier transform. We classify molecules into three types -- asymmetric, rotationally symmetric, and perrotationally symmetric -- with the last type having no macroscopic analogue due to nuclear-spin statistics constraints. We identify two features in perrotationally symmetric state spaces that are Hamiltonian-independent and induced solely by symmetry and spin statistics. First, many molecular species are intrinsically rotation-spin entangled in a way that cannot be broken without transitioning to another species or breaking symmetry. Second, each molecular position state houses an internal pseudo-spin or &quot;fiber&quot; degree of freedom, and the fiber&#39;s Berry phase or matrix after adiabatic changes in position yields naturally robust operations, akin to braiding anyonic quasiparticles or realizing fault-tolerant quantum gates. We outline scenarios where these features can be experimentally probed.</p>1 aAlbert, Victor, V.1 aKubischta, Eric1 aLemeshko, Mikhail1 aLiu, Lee, R.  uhttps://arxiv.org/abs/2403.04572